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Combining effects: sum and tensor
"... We seek a unified account of modularity for computational effects. We begin by reformulating Moggi’s monadic paradigm for modelling computational effects using the notion of enriched Lawvere theory, together with its relationship with strong monads; this emphasises the importance of the operations ..."
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Cited by 42 (5 self)
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We seek a unified account of modularity for computational effects. We begin by reformulating Moggi’s monadic paradigm for modelling computational effects using the notion of enriched Lawvere theory, together with its relationship with strong monads; this emphasises the importance of the operations that produce the effects. Effects qua theories are then combined by appropriate bifunctors on the category of theories. We give a theory for the sum of computational effects, which in particular yields Moggi’s exceptions monad transformer and an interactive input/output monad transformer. We further give a theory of the commutative combination of effects, their tensor, which yields Moggi’s sideeffects monad transformer. Finally we give a theory of operation transformers, for redefining operations when adding new effects; we derive explicit forms for the operation transformers associated to the above monad transformers.
Generic trace semantics via coinduction
 Logical Methods in Comp. Sci
, 2007
"... Abstract. Trace semantics has been defined for various kinds of statebased systems, notably with different forms of branching such as nondeterminism vs. probability. In this paper we claim to identify one underlying mathematical structure behind these “trace ..."
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Cited by 33 (10 self)
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Abstract. Trace semantics has been defined for various kinds of statebased systems, notably with different forms of branching such as nondeterminism vs. probability. In this paper we claim to identify one underlying mathematical structure behind these “trace
Probability and Nondeterminism in Operational Models of Concurrency
 In Proc. CONCUR, LNCS
, 2006
"... Abstract. We give a brief overview of operational models for concurrent systems that exhibit probabilistic behavior, focussing on the interplay between probability and nondeterminism. Our survey is carried out from the perspective of probabilistic automata, a model originally developed for the analy ..."
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Cited by 17 (1 self)
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Abstract. We give a brief overview of operational models for concurrent systems that exhibit probabilistic behavior, focussing on the interplay between probability and nondeterminism. Our survey is carried out from the perspective of probabilistic automata, a model originally developed for the analysis of randomized distributed algorithms. 1
Reasoning about probabilistic sequential programs ∗
"... A complete and decidable Hoarestyle calculus for iterationfree probabilistic sequential programs is presented using a state logic with truthfunctional propositional (not arithmetical) connectives. 1 ..."
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Cited by 16 (11 self)
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A complete and decidable Hoarestyle calculus for iterationfree probabilistic sequential programs is presented using a state logic with truthfunctional propositional (not arithmetical) connectives. 1
Continuous Previsions
"... We define strong monads of continuous (lower, upper) previsions, and of forks, modeling both probabilistic and nondeterministic choice. This is an elegant alternative to recent proposals by Mislove, Tix, Keimel, and Plotkin. We show that our monads are sound and complete, in the sense that they m ..."
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Cited by 9 (6 self)
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We define strong monads of continuous (lower, upper) previsions, and of forks, modeling both probabilistic and nondeterministic choice. This is an elegant alternative to recent proposals by Mislove, Tix, Keimel, and Plotkin. We show that our monads are sound and complete, in the sense that they model exactly the interaction between probabilistic and (demonic, angelic, chaotic) choice.
Probabilistic trueconcurrency models: branching cells and distributed probabilities, in "Information and Computation
, 2006
"... This paper is devoted to trueconcurrency models for probabilistic systems. By this we mean probabilistic models in which Mazurkiewicz traces, not interleavings, are given a probability. Here we address probabilistic event structures. We consider a new class of event structures, called locally finit ..."
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Cited by 9 (3 self)
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This paper is devoted to trueconcurrency models for probabilistic systems. By this we mean probabilistic models in which Mazurkiewicz traces, not interleavings, are given a probability. Here we address probabilistic event structures. We consider a new class of event structures, called locally finite. Locally finite event structures exhibit “finite confusion”; in particular, under some mild condition, confusionfree event structures are locally finite. In locally finite event structures, maximal configurations can be tiled with branching cells: branching cells are minimal and finite substructures capturing the choices performed while scanning a maximal configuration. A probabilistic event structure (p.e.s.) is a pair (E, P), where E is a prime event structure and P is a probability on the space of maximal configurations of E. We introduce the new class of distributed probabilities for p.e.s.: distributed probabilities are such that random choices in
Trueconcurrency probabilistic models Branching cells and distributed probabilities for event structures
, 2006
"... ..."
2013): Measurable spaces and their effect logic
 In: Logic in Computer Science, IEEE, Computer Science
"... Abstract—Socalled effect algebras and modules are basic mathematical structures that were first identified in mathematical physics, for the study of quantum logic and quantum probability. They incorporate a double negation law p⊥ ⊥ = p. Since then it has been realised that these effect structures ..."
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Cited by 8 (7 self)
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Abstract—Socalled effect algebras and modules are basic mathematical structures that were first identified in mathematical physics, for the study of quantum logic and quantum probability. They incorporate a double negation law p⊥ ⊥ = p. Since then it has been realised that these effect structures form a useful abstraction that covers not only quantum logic, but also Boolean logic and probabilistic logic. Moreover, the duality between effect and convex structures lies at the heart of the duality between predicates and states. These insights are leading to a uniform framework for the semantics of computation and logic. This framework has been elaborated elsewhere for settheoretic, discrete probabilistic, and quantum computation. Here the missing case of continuous probability is shown to fit in the same uniform framework. On a technical level, this involves an investigation of the logical aspects of the Giry monad on measurable spaces and of Lebesgue integration. KeywordsProbabilistic system, measurable space, Giry monad, effect algebra, duality.
Static Analysis of Programs with Imprecise Probabilistic Inputs
"... Abstract. Having a precise yet sound abstraction of the inputs of numerical programs is important to analyze their behavior. For many programs, these inputs are probabilistic, but the actual distribution used is only partially known. We present a static analysis framework for reasoning about prog ..."
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Cited by 3 (0 self)
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Abstract. Having a precise yet sound abstraction of the inputs of numerical programs is important to analyze their behavior. For many programs, these inputs are probabilistic, but the actual distribution used is only partially known. We present a static analysis framework for reasoning about programs with inputs given as imprecise probabilities: we define a collecting semantics based on the notion of previsions and an abstract semantics based on an extension of DempsterShafer structures. We prove the correctness of our approach and show on some realistic examples the kind of invariants we are able to infer. 1
2011): Relating direct and predicate transformer partial correctness semantics for an imperative probabilisticnondeterministic language
 Theor. Comp. Sci
"... In [KRS], based on [TKP, KP], a predicate transformer semantics has been derived from a direct total correctness semantics for a nondeterministic/probabilistic basic imperative programming language Lp whose syntax is given (in BNFform) ..."
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Cited by 2 (0 self)
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In [KRS], based on [TKP, KP], a predicate transformer semantics has been derived from a direct total correctness semantics for a nondeterministic/probabilistic basic imperative programming language Lp whose syntax is given (in BNFform)